CN112377594A - Sectional type point-line meshing gear pair - Google Patents

Sectional type point-line meshing gear pair Download PDF

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CN112377594A
CN112377594A CN202011247741.1A CN202011247741A CN112377594A CN 112377594 A CN112377594 A CN 112377594A CN 202011247741 A CN202011247741 A CN 202011247741A CN 112377594 A CN112377594 A CN 112377594A
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curve
involute
curve segment
gear
segment
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CN112377594B (en
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梁栋
孟胜
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Chongqing Jiaotong University
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Chongqing Jiaotong University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0806—Involute profile
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/0806—Involute profile
    • F16H55/0813—Intersecting-shaft arrangement of the toothed members

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)

Abstract

The invention relates to the technical field of gear transmission, in particular to a sectional point-line meshing gear pair which comprises a helical gear A and a helical gear B, wherein the tooth profile curve of the helical gear A comprises a convex arc curve section A1Short transition curve segment A2And an involute curve segment A3Short transition curve segment A2The upper end and the lower end of the arc-shaped groove are respectively connected with the convex arc curve section A in a smooth transition way1Lower end and involute curve segment A3The upper end of (a); the tooth profile curve of the bevel gear B comprises an involute curve section B1Short transition curve segment B2And a concave parabolic curve segment B3Short transition curve segment B2The upper end and the lower end of the sum are respectively connected with an involute curve section B in a smooth transition way1Lower end of (A) and a concave parabolic curve section B3The upper end of (a); convex arc curve segment A1Curve segment B of concave parabola3Form a curve segment A of double-point contact involute3Curve segment B of involute curve1Forming a line contact. The invention has both point contact form and wire contact form in the engaging process, and has the characteristics of high bearing capacity, low vibration noise, long service life and stable transmission.

Description

Sectional type point-line meshing gear pair
Technical Field
The invention relates to the technical field of gear transmission, in particular to a sectional type point-line meshing gear pair.
Background
The involute gear and the circular arc gear are widely applied due to the characteristics of line contact and point contact meshing respectively; currently, from the perspective of basic principles of gears, design modification, analysis process, manufacturing technology, and the like, many skilled in the art develop more beneficial researches to meet the performance requirements of mechanical equipment on high speed, heavy load, high reliability, long service life, low noise, and the like of a transmission system.
Patent 201410309538.0 proposes a design method of point contact double parabolic gear, which adopts two segments of parabolic segments and transition curve to form basic tooth profile, the designed point contact double parabolic gear transmission has separability, and when there is center distance error, the bearing capacity of the gear transmission will not be affected seriously; patent 201710858298.3 proposes a dotted line meshing helical gear pair with large bearing capacity and small vibration, which mainly adopts a modified helical gear mode and determines related parameters by combining the external meshing characteristic of helical gear nodes and the structural characteristics of dotted line meshing helical gears; patent 201610572270.9 proposes a curved-tooth-line point-line meshing gear and a processing method thereof, wherein the curved-tooth-line point-line meshing gear mainly adopts a modified involute gear form and combines a positive modification or negative modification method to realize the meshing characteristics of section point lines and lines; patent 201510579956.6 proposes a conjugate curve-based multi-point contact cylindrical gear meshing pair, the meshing mode is simultaneous multi-point contact between a convex tooth surface and a concave tooth surface, and the meshing pair has high bearing capacity and meshing stability; patent 201810558443.0 proposes a dotted-line meshing worm transmission mechanism, in which the worm, the transmission wheel and the helical rack all adopt tooth profiles of involute and arc, one half of the tooth height is the convex tooth profile of involute, and the other half is the concave tooth profile of transition curve. However, the existing point-line meshing gear pair has a single contact form, a complex design process of a point or line contact tooth profile, low bending/contact strength and high transmission noise, and cannot meet the requirements of current social production on high-bearing, high-efficiency and low-abrasion gears.
Therefore, a sectional point-line meshing gear pair is needed, which has both a point contact form and a line contact form in the meshing process and has the characteristics of high bearing capacity, low vibration noise, long service life and stable transmission.
Disclosure of Invention
In view of the above, the present invention provides a sectional point-line meshing gear pair, which has both a point contact type and a line contact type during the meshing process, and has the characteristics of high bearing capacity, low vibration noise, long service life, and smooth transmission.
In order to achieve the purpose, the invention provides a sectional dotted line meshing gear pair which comprises a helical gear A and a helical gear B, wherein the tooth profile curve of the helical gear A comprises a convex arc curve section A1Short transition curve segment A2And an involute curve segment A3Said short transition curve segment A2The upper end and the lower end of the arc-shaped groove are respectively connected with the convex arc curve section A in a smooth transition way1Lower end and involute curve segment A3The upper end of (a);
the tooth profile curve of the bevel gear B comprises an involute curve section B1Short transition curve segment B2And a concave parabolic curve segment B3Said short transition curve segment B2The upper end and the lower end of the sum are respectively connected with an involute curve section B in a smooth transition way1Lower end of (A) and a concave parabolic curve section B3The upper end of (a);
in the meshing process of the helical gear A and the helical gear B, the convex arc curve segment A1Curve segment B of concave parabola3Form a double-point contact, the involute curve segment A3Curve segment B of involute curve1Forming a line contact.
As a further improvement to the technical scheme of the invention, the tooth profile curve of the bevel gear A is a convex circular arc curve segment A1Is expressed as:
Figure BDA0002770605650000021
where ρ isaIs the tooth profile radius of a convex arc curve; alpha is alphaaIs the angle of the engagement parameter, satisfies alpha1≤αa≤α2；laIs from the center point of the convex arc curve to the coordinate axis xnThe distance of (d);
Figure BDA0002770605650000022
symbols respectively represent left and right side tooth surfaces;
the tooth profile curve middle-short transition curve section A of the helical gear A2Is expressed as:
Figure BDA0002770605650000031
where ρ iseaIs a short transition curve segment A2Corresponding to the tooth profile radius; thetaeaIs a short transition curve segment A2Upper position point parameter, having theta1≤θea≤θ2；αaThe same meaning, also meshing parameter angle;
involute curve section A in tooth profile curve of bevel gear A3Is expressed as:
Figure BDA0002770605650000032
wherein r is the base radius of bevel gear a;
Figure BDA0002770605650000033
is the parameter angle of the involute curve.
As a further improvement to the technical scheme of the invention, the tooth surface of the bevel gear A comprises a segment A which is curved with a convex circular arc1Short transition curve segment A2And an involute curve segment A3Convex arc tooth surface W in one-to-one correspondence1Short transition curve tooth surface W2And involute flank W3；
The convex arc tooth surface W1The equation of (a) is:
Figure BDA0002770605650000034
wherein r is1Is the pitch radius of the helical gear a;
Figure BDA0002770605650000035
is the angle of rotation of the bevel gear a after a period of time; u. ofaIs a space helical gear A coordinate system and a fixed seatDistance between the origin points of the systems; β is the gear helix angle;
the short transition curve tooth surface W2The equation of (a) is:
Figure BDA0002770605650000041
the involute tooth surface W3The equation of (a) is:
Figure BDA0002770605650000042
as a further improvement of the technical scheme of the invention, an involute curve section B in a tooth profile curve of the bevel gear B1Is expressed as:
Figure BDA0002770605650000043
wherein r' is the base radius of bevel gear B;
Figure BDA0002770605650000044
is the parameter angle of the involute curve;
Figure BDA0002770605650000046
symbols respectively represent left and right side tooth surfaces;
short transition curve section B of helical gear B2Is expressed as:
Figure BDA0002770605650000045
where ρ isea' is a short transition curve segment B2Corresponding to the tooth profile radius; thetaea' is a short transition curve segment B2Upper position point parameter, having theta1'≤θea'≤θ2'；αa' is the meshing parameter angle; rhocIs the tooth profile radius of the concave parabolic curve segment; lfIs a concave parabolic curveTooth profile center point to coordinate axis xnThe distance of (d);
concave parabola curve section B of the helical gear B3Is expressed as:
Figure BDA0002770605650000051
wherein t is a concave parabolic curve parameter; alpha is alphaεIs the engagement parameter angle; p is the helix parameter; theta is an included angle between a contact point on the concave parabola curve segment and the symmetrical center point of the parabola; the plus or minus symbols respectively represent the tooth surfaces at the left and right sides; j is the backlash.
As a further improvement to the technical scheme of the invention, the tooth surface of the bevel gear B comprises a curve section B which is in curve with an involute1Short transition curve segment B2And a concave parabolic curve segment B3Involute tooth surface M in one-to-one correspondence1Short transition curve tooth surface M2And concave parabolic tooth surface M3；
The involute tooth surface M1The equation of (a) is:
Figure BDA0002770605650000052
wherein r is2Is the pitch radius of bevel gear B;
Figure BDA0002770605650000053
is the angle of rotation of the bevel gear B after a period of time; u. offThe distance between the spatial helical gear B coordinate system and the fixed coordinate system origin is shown; β is the gear helix angle;
the short transition curve tooth surface M2The equation of (a) is:
Figure BDA0002770605650000054
the concave parabolic tooth surface M3The equation of (a) is:
Figure BDA0002770605650000061
compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a novel sectional type point-line meshing gear pair combining an involute tooth profile contact characteristic and an arc-parabola convex-concave double-point contact characteristic, which not only inherits the advantages of divisible involute tooth profile center distance and simplicity and convenience in manufacturing, but also has the advantages of high arc-parabola convex-concave tooth profile double-point contact bearing capacity, high transmission efficiency and small friction and abrasion in the meshing process, and solves the problems of single contact form, complex design process of point or line contact tooth profiles, low bending/contact strength and high transmission noise of the existing point-line meshing gear pair.
Drawings
FIG. 1 is a schematic basic tooth profile of a bevel gear A of a segmented point-and-line meshing gear pair according to the present invention;
FIG. 2 is a sectional short transition curve section A of the basic tooth profile of a bevel gear A in a dotted line meshing gear pair according to the present invention2Solving the schematic diagram;
FIG. 3 is a schematic view illustrating a process of forming a tooth surface of a bevel gear A in a segmented point-line meshing gear pair according to the present invention;
FIG. 4 is a schematic basic tooth profile of a bevel gear B of a segmented point-and-line meshing gear pair according to the present invention;
FIG. 5 is a schematic view illustrating a process of forming a tooth surface of a bevel gear B in a segmented point-line meshing gear pair according to the present invention;
FIG. 6 is a schematic view of the tooth surface contact of a segmented point-line meshing gear pair according to the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific examples.
As shown in fig. 1 to 6: the embodiment provides a sectional dotted-line meshing gear pair which comprises a bevel gear A1 and a bevel gear B2, wherein the bevel gear A1The tooth profile curve comprises a convex arc curve segment A1Short transition curve segment A2And an involute curve segment A3Said short transition curve segment A2The upper end and the lower end of the arc-shaped groove are respectively connected with the convex arc curve section A in a smooth transition way1Lower end and involute curve segment A3The upper end of (a); the tooth profile curve of the bevel gear B2 comprises an involute curve section B1Short transition curve segment B2And a concave parabolic curve segment B3Said short transition curve segment B2The upper end and the lower end of the sum are respectively connected with an involute curve section B in a smooth transition way1Lower end of (A) and a concave parabolic curve section B3The upper end of (a); when the helical gear A1 is meshed with the helical gear B2, the convex arc curve segment A1Curve segment B of concave parabola3Form a double-point contact, the involute curve segment A3Curve segment B of involute curve1Forming a line contact.
As shown in FIG. 1, a basic tooth profile schematic diagram of a bevel gear A1 in a sectional dotted-line meshing gear pair is established, and a convex circular arc curve section A in a tooth profile curve of the bevel gear A11Is expressed as:
Figure BDA0002770605650000071
where ρ isaIs the tooth profile radius of a convex arc curve; alpha is alphaαIs the angle of the engagement parameter, satisfies alpha1≤αα≤α2；lαIs from the center point of the convex arc curve to the coordinate axis xnThe distance of (d);
Figure BDA0002770605650000072
symbols respectively represent left and right side tooth surfaces;
short transition curve segment A2Connecting a convex arc curve segment A for smooth transition1And an involute curve segment A3A portion of (a), which does not participate in the engagement process; as shown in FIG. 2, the over-convex arc curve segment A is calculated first1Lower endpoint k3Tangent line T of2And an over-involute curve segment A3Upper endpoint k2Tangent line T of1Secondly, two tangent lines T are obtained1、T2Through the two end points k, is calculated again2、k3And is in contact with two tangent lines T1、T2A common tangent curve satisfying:
Figure BDA0002770605650000081
in a coordinate system SnThe middle short transition curve section A of the tooth profile curve of the bevel gear A12Is expressed as:
Figure BDA0002770605650000082
where ρ iseaIs a short transition curve segment A2Corresponding to the tooth profile radius; thetaeaIs a short transition curve segment A2Upper position point parameter, having theta1≤θea≤θ2；ααThe same meaning, also meshing parameter angle;
in a coordinate system SnThe involute curve section A in the tooth profile curve of the bevel gear A13Is expressed as:
Figure BDA0002770605650000083
where r is the base radius of bevel gear A1;
Figure BDA0002770605650000084
is the parameter angle of the involute curve.
As shown in FIG. 3, a tooth surface forming coordinate system of the helical gear A1 is established, an engaging tooth surface is established by a rack forming method, and a space fixing coordinate system S is established0(O0-x0,y0,z0) Connected with the gear in a movable coordinate system Sp(Op-xp,yp,zp) And S1(O1-x1,y1,z1) Respectively fixedly connected with a rack cutter and a gear and a coordinate system Sn(On-xn,yn,zn) And is also fixedly connected with the rack cutter. Coordinate axis znAnd zpThe included angle between the gear and the gear is the helical angle beta of the gear and the origin of coordinates OnAnd OpThe distance between the two is u, and the radius of the gear pitch cylinder is r1. At the same time, the rack tool follows the coordinate axis ypIn the negative direction of (v) is linear velocity vpMoving while the gear blank is at an angular velocity omega1Along a coordinate axis z0And when the rack cutter rotates anticlockwise, the pitch plane of the rack cutter is tangent to the pitch cylinder of the gear. When the gear blank rotates anticlockwise
Figure BDA0002770605650000091
When the rack cutter moves leftwards by a distance
Figure BDA0002770605650000092
From the coordinate system SnTo a coordinate system SpThe general transformation relationship of (1) is:
Figure BDA0002770605650000093
from the coordinate system SpTo a coordinate system S1The general transformation relationship of (1) is:
Figure BDA0002770605650000094
obtaining a tooth surface equation of the bevel gear A1 by utilizing the principle of gear geometry and through coordinate relation transformation and tooth surface meshing equation derivation, wherein the tooth surface of the bevel gear A1 comprises a segment A of a convex arc curve1Short transition curve segment A2And an involute curve segment A3Convex arc tooth surface W in one-to-one correspondence1Short transition curve tooth surface W2And involute flank W3；
The convex arc tooth surface W1The equation of (a) is:
Figure BDA0002770605650000095
wherein r is1Is the pitch radius of helical gear a 1;
Figure BDA0002770605650000096
is the angle of rotation of bevel gear a1 after a period of time; u. ofaIs the distance between the spatial helical gear A1 coordinate system and the fixed coordinate system origin; β is the gear helix angle;
the short transition curve tooth surface W2The equation of (a) is:
Figure BDA0002770605650000101
the involute tooth surface W3The equation of (a) is:
Figure BDA0002770605650000102
as shown in FIG. 4, a basic tooth profile schematic diagram of a bevel gear B2 in a sectional dotted-line meshing gear pair is established, and an involute curve section B in a tooth profile curve of the bevel gear B21Is expressed as:
Figure BDA0002770605650000103
wherein r' is the base radius of bevel gear B2;
Figure BDA0002770605650000104
is the parameter angle of the involute curve;
Figure BDA0002770605650000106
symbols respectively represent left and right side tooth surfaces;
in the same way, the middle short transition curve section B of the tooth profile curve of the bevel gear B22The derivation process is similar, the involute curve is calculated firstLine segment B1Tangent line of lower end point, over-concave parabola curve segment B3The tangent line of the upper end point, then the common intersection point of the two tangent lines is obtained, and the curve which passes through the two end points and is commonly tangent with the two tangent lines is calculated again, thereby obtaining the short transition curve section B2(ii) a In a coordinate system SnShort transition curve section B of helical gear B22Is expressed as:
Figure BDA0002770605650000105
where ρ isea' is a short transition curve segment B2Corresponding to the tooth profile radius; thetaea' is a short transition curve segment B2Upper position point parameter, having theta1'≤θea'≤θ2'；αα' is the meshing parameter angle; rhocIs the tooth profile radius of the concave parabolic curve segment; lfIs from the central point of the tooth profile of the concave parabolic curve to the coordinate axis xnThe distance of (d);
in a coordinate system SnLower, concave parabolic curve segment B of said helical gear B23Is expressed as:
Figure BDA0002770605650000111
wherein t is a concave parabolic curve parameter; alpha is alphaeIs the engagement parameter angle; p is the helix parameter; theta is an included angle between a contact point on the concave parabola curve segment and the symmetrical center point of the parabola; the plus or minus symbols respectively represent the tooth surfaces at the left and right sides; j is the backlash.
As shown in FIG. 5, a tooth surface forming coordinate system of the helical gear B2 is established, an engaging tooth surface is established by a rack forming method, and a space fixing coordinate system S is establishedu(Ou-xu,yu,zu) Connected with the gear in a movable coordinate system Sp(Op-xp,yp,zp) And S2(O2-x2,y2,z2) Respectively fixedly connected with the rack cutter and the gearMarker series Sn(On-xn,yn,zn) And is also fixedly connected with the rack cutter. The radius of the gear pitch cylinder is r2. At the same time, the rack tool follows the coordinate axis ypIn the negative direction of (v) is linear velocity vpMoving while the gear blank is at an angular velocity omega2Along a coordinate axis zuAnd when the rack cutter rotates clockwise, the pitch plane of the rack cutter is tangent to the pitch cylinder of the gear. When the gear blank rotates clockwise
Figure BDA0002770605650000112
When the rack cutter moves leftwards by a distance
Figure BDA0002770605650000113
From the coordinate system SnTo a coordinate system SpThe general transformation relationship of (1) is:
Figure BDA0002770605650000114
from the coordinate system SpTo a coordinate system S2The general transformation relationship of (1) is:
Figure BDA0002770605650000121
obtaining a tooth surface equation of a bevel gear B2 by utilizing the principle of gear geometry and through coordinate relation transformation and tooth surface meshing equation derivation, wherein the tooth surface of the bevel gear B2 comprises a curve segment B with an involute1Short transition curve segment B2And a concave parabolic curve segment B3Involute tooth surface M in one-to-one correspondence1Short transition curve tooth surface M2And concave parabolic tooth surface M3；
The involute tooth surface M1The equation of (a) is:
Figure BDA0002770605650000122
wherein the content of the first and second substances,r2is the pitch radius of helical gear B2;
Figure BDA0002770605650000123
is the angle of rotation of bevel gear B2 after a period of time; u. offIs the distance between the spatial helical gear B2 coordinate system and the fixed coordinate system origin; β is the gear helix angle;
the short transition curve tooth surface M2The equation of (a) is:
Figure BDA0002770605650000124
the concave parabolic tooth surface M3The equation of (a) is:
Figure BDA0002770605650000131
FIG. 6 is a schematic view of the tooth surface contact of a segmented dotted meshing gear pair with a bevel gear A1 obtained for proper mating engagement with the tooth surface of a bevel gear B2, showing the convex arcuate curved line segment A of bevel gear A11Concave parabolic curve section B of bevel gear B23Form a double-point contact, and an involute curve section A in a helical gear A13Involute curve section B of bevel gear B21The line contacts are configured so that a combination of the two properties is achieved during engagement.
The embodiment provides a novel sectional type point-line meshing gear pair combining involute tooth profile contact characteristics and arc-parabola convex-concave double-point contact characteristics, and the gear pair has the advantages of divisible involute tooth profile center distance and simplicity and convenience in manufacturing in the meshing process, has the advantages of high arc-parabola convex-concave tooth profile double-point contact bearing capacity, high transmission efficiency and small friction and wear, and solves the problems that the existing point-line meshing gear pair is single in contact form, complex in design process of point-line or linear contact tooth profiles, low in bending/contact strength and large in transmission noise.
Finally, the principle and embodiments of the present invention are explained by using specific examples, and the above descriptions of the examples are only used to help understand the core idea of the present invention, and the present invention can be modified and modified without departing from the principle of the present invention, and the modified and modified examples also fall into the protection scope of the present invention.

Claims (5)

1. A sectional type point-line meshing gear pair comprises a bevel gear A and a bevel gear B, and is characterized in that:
the tooth profile curve of the helical gear A comprises a convex arc curve segment A1Short transition curve segment A2And an involute curve segment A3Said short transition curve segment A2The upper end and the lower end of the arc-shaped groove are respectively connected with the convex arc curve section A in a smooth transition way1Lower end and involute curve segment A3The upper end of (a);
the tooth profile curve of the bevel gear B comprises an involute curve section B1Short transition curve segment B2And a concave parabolic curve segment B3Said short transition curve segment B2The upper end and the lower end of the sum are respectively connected with an involute curve section B in a smooth transition way1Lower end of (A) and a concave parabolic curve section B3The upper end of (a);
in the meshing process of the helical gear A and the helical gear B, the convex arc curve segment A1Curve segment B of concave parabola3Form a double-point contact, the involute curve segment A3Curve segment B of involute curve1Forming a line contact.
2. The segmented dotted meshing gear pair of claim 1, wherein: the tooth profile curve of the helical gear A is a convex circular arc curve section A1Is expressed as:
Figure FDA0002770605640000011
where ρ isaIs the tooth profile radius of a convex arc curve; alpha is alphaαIs the angle of the engagement parameter, satisfies alpha1≤αα≤α2；lαIs from the center point of the convex arc curve to the coordinate axis xnThe distance of (d);
Figure FDA0002770605640000013
symbols respectively represent left and right side tooth surfaces;
the tooth profile curve middle-short transition curve section A of the helical gear A2Is expressed as:
Figure FDA0002770605640000012
where ρ iseaIs a short transition curve segment A2Corresponding to the tooth profile radius; thetaeaIs a short transition curve segment A2Upper position point parameter, having theta1≤θea≤θ2；ααThe same meaning, also meshing parameter angle;
involute curve section A in tooth profile curve of bevel gear A3Is expressed as:
Figure FDA0002770605640000021
wherein r is the base radius of bevel gear a;
Figure FDA0002770605640000022
is the parameter angle of the involute curve.
3. The segmented dotted meshing gear pair of claim 2, wherein: the tooth surface of the helical gear A comprises a convex arc curve segment A1Short transition curve segment A2And an involute curve segment A3Convex arc tooth surface W in one-to-one correspondence1Short transition curve tooth surface W2And involute flank W3；
The convex arc tooth surface W1The equation of (a) is:
Figure FDA0002770605640000023
wherein r is1Is the pitch radius of the helical gear a;
Figure FDA0002770605640000024
is the angle of rotation of the bevel gear a after a period of time; u. ofaThe distance between the space helical gear A coordinate system and the fixed coordinate system origin is shown; β is the gear helix angle;
the short transition curve tooth surface W2The equation of (a) is:
Figure FDA0002770605640000025
the involute tooth surface W3The equation of (a) is:
Figure FDA0002770605640000026
4. the segmented dotted meshing gear pair of claim 1, wherein: involute curve section B in tooth profile curve of bevel gear B1Is expressed as:
Figure FDA0002770605640000031
wherein r' is the base radius of bevel gear B;
Figure FDA0002770605640000032
is the parameter angle of the involute curve;
Figure FDA0002770605640000035
symbols respectively represent left and right side tooth surfaces;
short transition curve section B of helical gear B2Is expressed as:
Figure FDA0002770605640000033
where ρ isea' is a short transition curve segment B2Corresponding to the tooth profile radius; thetaea' is a short transition curve segment B2Upper position point parameter, having theta1'≤θea'≤θ2'；αa' is the meshing parameter angle; rhocIs the tooth profile radius of the concave parabolic curve segment; lfIs from the central point of the tooth profile of the concave parabolic curve to the coordinate axis xnThe distance of (d);
concave parabola curve section B of the helical gear B3Is expressed as:
Figure FDA0002770605640000034
wherein t is a concave parabolic curve parameter; alpha is alphaεIs the engagement parameter angle; p is the helix parameter; theta is an included angle between a contact point on the concave parabola curve segment and the symmetrical center point of the parabola; the plus or minus symbols respectively represent the tooth surfaces at the left and right sides; j is the backlash.
5. The segmented dotted meshing gear pair of claim 4, wherein: the tooth surface of the bevel gear B comprises a curve section B which is in curve with an involute1Short transition curve segment B2And a concave parabolic curve segment B3Involute tooth surface M in one-to-one correspondence1Short transition curve tooth surface M2And concave parabolic tooth surface M3；
The involute tooth surface M1The equation of (a) is:
Figure FDA0002770605640000041
wherein r is2Is the pitch radius of bevel gear B;
Figure FDA0002770605640000042
is the angle of rotation of the bevel gear B after a period of time; u. offThe distance between the spatial helical gear B coordinate system and the fixed coordinate system origin is shown; β is the gear helix angle;
the short transition curve tooth surface M2The equation of (a) is:
Figure FDA0002770605640000043
the concave parabolic tooth surface M3The equation of (a) is:
Figure FDA0002770605640000044
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